write expression sin(3x) cos(2x) as a sum or difference

[Dmoney1578]

Do know how to do this problem Write the following experssion as a sum or difference: sin(3x) cos(2x)

 

[skeeter]

check the problem statement again ... I believe the expression is incomplete as posted.

never mind ... I had
sin(3x)cos(2x) +/- cos(3x)sin(2x) = sin(3x +/- 2x)
on my mind.

 

[soroban]

Hello, Dmoney1578!

Write the following experssion as a sum or difference: .\(\displaystyle \sin(3x)\cos(2x)\)

\(\displaystyle \text{We need a product-to-sum identity: }\;\sin A\cos B \:=\:\frac{1}{2}\bigg[\sin(A-B) + \sin(A+B)\bigg]\)

\(\displaystyle \text{Therefore: }\;\sin(3x)\cos(2x) \;=\;\frac{1}{2}\bigg[\sin(x) + \sin(5x)\bigg]\)